two pulley rotate at 150 rpm and 300 rpm. the diameter of the larger pulley 15cm if the pulley are connected by belt . what is the diameter of the smaller pulley.
Since the distance covered by the belt depends on the circumference of the circles , ...
150(2π(15)) = 300(2πr)
15π = 2πr
r = 15/2 = 7.5 cm
or
the speed of the pulleys is inversely proportional to the their radii
r/15 = 300/150
r/15 = 2
2r = 15
r = 7.5
To find the diameter of the smaller pulley, we can use the formula for the speed ratio between two pulleys connected by a belt:
Speed ratio = RPM of Larger Pulley / RPM of Smaller Pulley
In this case, the RPM of the larger pulley is given as 150, and the RPM of the smaller pulley is unknown. Let's say it's x.
So, the speed ratio becomes:
150 / x = 300 / 150
Now, we can solve for x:
150 / x = 2
Cross-multiplying:
150 = 2x
Dividing both sides by 2:
x = 150 / 2 = 75
Therefore, the RPM of the smaller pulley is 75.
Next, we can use the formula for the speed ratio between pulleys to find the diameter of the smaller pulley:
Speed ratio = Diameter of Larger Pulley / Diameter of Smaller Pulley
Using the given diameter of the larger pulley as 15 cm and the calculated RPMs, the formula becomes:
150 / 75 = 15 / D
Cross-multiplying:
150D = 75 * 15
150D = 1125
Dividing both sides by 150:
D = 1125 / 150
D = 7.5 cm
Therefore, the diameter of the smaller pulley is 7.5 cm.
To find the diameter of the smaller pulley, we need to use the concept of Belt and Pulley Speed Ratio.
The speed ratio of two pulleys connected by a belt is equal to the ratio of their rotational speeds.
Here, the speed of the larger pulley is 150 rpm, and the speed of the smaller pulley is 300 rpm.
Now, let's assume the diameter of the smaller pulley is D cm.
The speed ratio can be determined by dividing the speed of the larger pulley by the speed of the smaller pulley:
Speed Ratio = Speed of Larger Pulley / Speed of Smaller Pulley
Speed Ratio = 150 rpm / 300 rpm
Simplifying, we get:
Speed Ratio = 1/2
Now, let's relate the speed ratio to the diameters of the pulleys. The speed ratio is also equal to the ratio of the diameters of the pulleys.
Speed Ratio = Diameter of Larger Pulley / Diameter of Smaller Pulley
1/2 = 15 cm / D cm
To find D, we can rearrange the equation:
D cm = 15 cm / (1/2)
D cm = 15 cm * 2
D cm = 30 cm
Therefore, the diameter of the smaller pulley is 30 cm.